Now I might lose first round because my enthusiasm is on 12 and some team that is much weaker them mine win because they accumulated 15 by random.
It will be impossible for them to play with above 12 enthusiasm in the first round. Using the coach parrot spreadsheet's enthusiasm calculator tool, which I've found to be highly accurate in matching my enthusiasm, if a team has played TIE every match of the season and was still playing Cup matches on last Thursday, they will play the first round of the playoffs with 11.1 enthusiasm.
I think you may be experiencing confusion with how it works. When you play TIE, your enthusiasm immediately after the game will be increased by one third. If you attempt to set your lineup for a future game once the game has simulated, you will see the updated level at that time. Every day when team updates process, enthusiasm levels trend back to 5, with higher drops at higher levels, so that if you hit 15 enthusiasm on game night, it'll drop to 12 within a couple of days. Fortunately, this also applies to your opponents, so you won't run into someone with a 15.
The main takeaway, though, is that it is entirely not random. The formula has been reverse engineered or at least a very close approximation, so rest assured that if you lose to worse opponents, it won't be because of randomness in enthusiasm.